Dr. F. Tinker on Osmotic Pressure. 411 



must be limited to the case in which two non-ideal dilute 

 solutions of equal concentration are placed on opposite sides 

 of the membrane. Subject to this limitation Traube's 

 surface-tension theory will no doubt continue to be of great 

 value, even as it has proved to be in the past. The scope of 

 Traube's theory, limited as above, would apparently be 

 extensive*, for most actual solutions are more or less non- 

 ideal. 



We can now sketch briefly the general theory of osmotic 

 flow. It is evident that if two solutions (each under the 

 same hydrostatic pressure) are on opposite sides of a 

 membrane, the solvent will flow from the one which 

 generates the greater pressure f inside the membrane, i. e. 

 from the one which has also the greater partial (solvent) 

 vapour pressure. Now, the pressure generated by each 

 solution in either the membrane or the vapour phase proper 

 is determined partly by the liquid pressure 7r/ of the solvent 

 inside the solution and partly by the work factor A x ' ; so 

 that we can regard the magnitude and direction of osmotic 

 flow as being caused ultimately by differences in the value 

 of 77-/ and A/ for the two solutions. If the differences in 

 the value of Ax' are nil, the osmotic flow is thus determined 

 entirely by the differences in 77-/, the direction of the flow 

 obviously proceeding from the solution in which the solvent 

 has the higher fluid pressure to the one in which it has the 

 lower fluid pressure %. If, on the other hand, the differences 

 in 7Ti' are eliminated, as by working with dilute solutions of 

 equal concentration on opposite sides of the membrane, the 

 direction of flow is determined entirely by the differences in 

 the value of A/, i. e. (and as shown above) by the differences 

 in heats of dilution, intrinsic pressure, surface-tension, &c. 



The problem can be resolved even still further. The 

 pressure of the solvent inside a solution is itself determined 

 by its molar fraction and also by the change in volume which 

 it undergoes during the process of solution (equation [2] 

 p. 432) ; so that in the general case we can state that the 



* Cf. Macallum, Brit. Assoc. Reports, 1910, p. 740. It is clear also 

 that in the case we have been considering the velocity of osmosis will be 

 determined largely by intrinsic pressure (and surface-tension) differences 

 between the two solutions. In this connexion it is interesting to note 

 that Prof. Adrian Brown and the author have found that the rate of 

 osmotic flow into barley seeds becomes greater as the surface-tension 

 of the outside solution diminishes. (Proc. Hoy. Soc, B. lxxxix. p. 119 

 (1915).) 



t /• e. partial pressure of the solvent. 



% Tinker, ■ Nature,' xcvii. p. 122 (1916). This idea of osmosis 

 being determined by magnitude of the fluid pressure of the solvent 

 seems to have been foreshadowed by Porter (Proc. Roy. Soc. A. lxxx. 

 p. 457 (1908), Addendum to paper). 



